HYPOT(3) BSD Library Functions Manual HYPOT(3)
hypot, hypotf -- Euclidean distance and complex absolute value functions
Math Library (libm, -lm)
hypot(double x, double y);
hypotf(float x, float y);
The hypot() functions compute the sqrt(x*x+y*y) in such a way that underflow will not hap-
pen, and overflow occurs only if the final result deserves it.
hypot(infinity, v) = hypot(v, infinity) = +infinity for all v, including NaN.
Below 0.97 ulps. Consequently hypot(5.0, 12.0) = 13.0 exactly; in general, hypot returns an
integer whenever an integer might be expected.
The same cannot be said for the shorter and faster version of hypot that is provided in the
comments in cabs.c; its error can exceed 1.2 ulps.
As might be expected, hypot(v, NaN) and hypot(NaN, v) are NaN for all finite v; with
"reserved operand" in place of "NaN", the same is true on a VAX. But programmers on
machines other than a VAX (it has no infinity) might be surprised at first to discover that
hypot(+-infinity, NaN) = +infinity. This is intentional; it happens because hypot(infinity,
v) = +infinity for all v, finite or infinite. Hence hypot(infinity, v) is independent of v.
Unlike the reserved operand fault on a VAX, the IEEE NaN is designed to disappear when it
turns out to be irrelevant, as it does in hypot(infinity, NaN).
Both a hypot() function and a cabs() function appeared in Version 7 AT&T UNIX. cabs() was
removed from public namespace in NetBSD 5.0 to avoid conflicts with the complex function in
BSD February 12, 2007 BSD